{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:33PJREM5N6GKRIB3QSALO5BJZT","short_pith_number":"pith:33PJREM5","schema_version":"1.0","canonical_sha256":"dede98919d6f8ca8a03b8480b77429ccce1f3e7f1f1feb43a3e81d7930354969","source":{"kind":"arxiv","id":"1501.06457","version":1},"attestation_state":"computed","paper":{"title":"The Schur-Horn Problem for Normal Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Matthew Kennedy, Paul Skoufranis","submitted_at":"2015-01-26T16:13:27Z","abstract_excerpt":"We consider the Schur-Horn problem for normal operators in von Neumann algebras, which is the problem of characterizing the possible diagonal values of a given normal operator based on its spectral data. For normal matrices, this problem is well-known to be extremely difficult, and in fact, it remains open for matrices of size greater than $3$. We show that the infinite dimensional version of this problem is more tractable, and establish approximate solutions for normal operators in von Neumann factors of type I$_\\infty$, II and III. A key result is an approximation theorem that can be seen as"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.06457","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-01-26T16:13:27Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"993b85829c7f5ed811141358fd38505b9f1d6ba47c66bc9b3d8c2357bd4b3c05","abstract_canon_sha256":"c32778e069bd511c2279d3ec1bc6e4aa9852041e273b7ba71f64d4e615556109"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:03.742750Z","signature_b64":"lK6RnUKriZQbBVnXUT6l2Boi7j4AUOxCx9KQXDM3q7RkGitTSRarVpSu2BRx5UcRWpXJLfYUAoTZ3iRmFTm/Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dede98919d6f8ca8a03b8480b77429ccce1f3e7f1f1feb43a3e81d7930354969","last_reissued_at":"2026-05-18T01:29:03.742168Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:03.742168Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Schur-Horn Problem for Normal Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Matthew Kennedy, Paul Skoufranis","submitted_at":"2015-01-26T16:13:27Z","abstract_excerpt":"We consider the Schur-Horn problem for normal operators in von Neumann algebras, which is the problem of characterizing the possible diagonal values of a given normal operator based on its spectral data. For normal matrices, this problem is well-known to be extremely difficult, and in fact, it remains open for matrices of size greater than $3$. We show that the infinite dimensional version of this problem is more tractable, and establish approximate solutions for normal operators in von Neumann factors of type I$_\\infty$, II and III. A key result is an approximation theorem that can be seen as"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.06457","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1501.06457","created_at":"2026-05-18T01:29:03.742262+00:00"},{"alias_kind":"arxiv_version","alias_value":"1501.06457v1","created_at":"2026-05-18T01:29:03.742262+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.06457","created_at":"2026-05-18T01:29:03.742262+00:00"},{"alias_kind":"pith_short_12","alias_value":"33PJREM5N6GK","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_16","alias_value":"33PJREM5N6GKRIB3","created_at":"2026-05-18T12:29:02.477457+00:00"},{"alias_kind":"pith_short_8","alias_value":"33PJREM5","created_at":"2026-05-18T12:29:02.477457+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/33PJREM5N6GKRIB3QSALO5BJZT","json":"https://pith.science/pith/33PJREM5N6GKRIB3QSALO5BJZT.json","graph_json":"https://pith.science/api/pith-number/33PJREM5N6GKRIB3QSALO5BJZT/graph.json","events_json":"https://pith.science/api/pith-number/33PJREM5N6GKRIB3QSALO5BJZT/events.json","paper":"https://pith.science/paper/33PJREM5"},"agent_actions":{"view_html":"https://pith.science/pith/33PJREM5N6GKRIB3QSALO5BJZT","download_json":"https://pith.science/pith/33PJREM5N6GKRIB3QSALO5BJZT.json","view_paper":"https://pith.science/paper/33PJREM5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1501.06457&json=true","fetch_graph":"https://pith.science/api/pith-number/33PJREM5N6GKRIB3QSALO5BJZT/graph.json","fetch_events":"https://pith.science/api/pith-number/33PJREM5N6GKRIB3QSALO5BJZT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/33PJREM5N6GKRIB3QSALO5BJZT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/33PJREM5N6GKRIB3QSALO5BJZT/action/storage_attestation","attest_author":"https://pith.science/pith/33PJREM5N6GKRIB3QSALO5BJZT/action/author_attestation","sign_citation":"https://pith.science/pith/33PJREM5N6GKRIB3QSALO5BJZT/action/citation_signature","submit_replication":"https://pith.science/pith/33PJREM5N6GKRIB3QSALO5BJZT/action/replication_record"}},"created_at":"2026-05-18T01:29:03.742262+00:00","updated_at":"2026-05-18T01:29:03.742262+00:00"}